A central question in ecology is to understand the ecological processes that shape community structure. Niche-based theories have emphasized the important role played by competition for maintaining species diversity. Many of these insights have been derived using MacArthur's consumer resource model (MCRM) or its generalizations. Most theoretical work on the MCRM has focused on small ecosystems with a few species and resources. However theoretical insights derived from small ecosystems many not scale up large ecosystems with many resources and species because large systems with many interacting components often display new emergent behaviors that cannot be understood or deduced from analyzing smaller systems. To address these shortcomings, we develop a statistical physics inspired cavity method to analyze MCRM when both the number of species and the number of resources is large. Unlike previous work in this limit, our theory addresses resource dynamics and resource depletion and demonstrates that species generically and consistently perturb their environments and significantly modify available ecological niches. We show how our cavity approach naturally generalizes niche theory to large ecosystems by accounting for the effect of collective phenomena on species invasion and ecological stability. Our theory suggests that such phenomena are a generic feature of large, natural ecosystems and must be taken into account when analyzing and interpreting community structure. It also highlights the important role that statistical-physics inspired approaches can play in furthering our understanding of ecology.

中文翻译：

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群落生态学的统计物理学：麦克阿瑟消费者资源模型的空腔解决方案

生态学的一个核心问题是理解塑造群落结构的生态过程。基于生态位的理论强调了竞争对于维持物种多样性所发挥的重要作用。其中许多见解都是通过麦克阿瑟的消费者资源模型 (MCRM) 或其概括得出的。大多数关于 MCRM 的理论工作都集中在具有少数物种和资源的小型生态系统。然而，源自小型生态系统的理论见解许多无法扩大具有许多资源和物种的大型生态系统，因为具有许多相互作用组件的大型系统通常会表现出新的突发行为，而这些行为无法通过分析较小的系统来理解或推断。为了解决这些缺点，我们开发了一种受统计物理启发的空腔方法，用于在物种数量和资源数量都很大时分析 MCRM。与之前在这一限制方面的研究不同，我们的理论解决了资源动态和资源枯竭问题，并证明物种普遍且持续地扰乱其环境并显着改变可用的生态位。我们展示了我们的空洞方法如何通过考虑集体现象对物种入侵和生态稳定性的影响，自然地将生态位理论推广到大型生态系统。我们的理论表明，这种现象是大型自然生态系统的普遍特征，在分析和解释群落结构时必须考虑到这一点。它还强调了统计物理学启发的方法在加深我们对生态学的理解方面可以发挥的重要作用。